you are probably refering to this image
in the tutorial here. Right?
The reason why you don't see this, is probably that you want to stop syncing the
~/Ubuntu One folder, which is always in sync. Only additional folders which are synced from elsewhere in your file system can be turned on/off.
(And I don't know what your last sentence: "I need to turn off syncing in order to store data off my computer in Ubuntu One." means. Maybe you could be more specific on what you need and why you need to turn off syncing for this?)
EDIT: Ubuntu One is not designed to store your data online, it is designed to synchronize data between your computers. Therefore you will not be able to keep a folder in Ubuntu One if you don't have it synchronized to any of your computers.
"Stop syncing" on the Ubuntu One website gives you a warning that the folders will NOT be deleted on your computer, but it will no longer be on the Ubuntu One servers.
If you have many computers, you can on each computer start/stop synchronizing the folders via Nautilus (the file manager) or via the Ubuntu One control panel (start e.g. via the mail icon in the panel and then "Ubuntu One"). Stopping via those ways does not remove the folders on the Ubuntu One servers, unless this was the only computer syncing that specific folder.
Its not completely straight forward, but you will understand it, if you remember that the Ubuntu One files service is only intended for syncing, not for storing data.